As has been mentioned already, Gygax and pals stole stuff from everything they'd read, and they read a lot more than Tolkien. The myth that D&D began as a straight D&D lift came from people who'd only read Tolkien so they didn't know any better. Sadly, the power of suggestion being what it is, many people who should know better have bought into that ... nodding their heads and saying "yep" when they see a Tolkienesque element.
Others here have mentioned that the magic comes from Vance, and that Ioun stones do, too. Hmm, didn't know about the stones. Never been able to finish reading anything by Jack Vance, so I don't start anymore. My favorite example of how someone other than JRRT should have been able to sue Gary into poverty is Poul Anderson's "Three Hearts and Three Lions", which has characters that are clearly the original Paladin, Nixie, Gnome (called a "Hill Dwarf", but the big nose and foresty dwellings are no coincidence) and Troll. When I read the novel, my one bit of confusion was why the Swanmay wasn't stolen too ... a month later, the 1e MM-2 came out, there she was. Anderson is also the only place I've seen the word "drow" in a source prior to D&D, in a book called "The Broken Sword".
Exposition about Law vs. Chaos is, of course, the influence of Moorcock. Everyone knows that.
The 1e DMG has a section that lists Vance, Anderson, Moorcock, Howard, and several others as it's sources. The creators of the game never claimed to have come up with themselves, and they never claimed to use a single source. And they told you to go ahead and change all the stuff you didn't like, whether it was the stuff they stole or not.
As for the origin of the Tolkien orc ... he surely knew about the orcneas of Beowulf, but I've always been a bit suspicious of another source. There was a tribe in Ireland of old called the Orcs, and JRRT, an englishman who was surely exposed to certain stereotypical ideas about the Irish, portrays the orcs as a bunch of lazy, stupid drunks who are always ready for a fight. And if my suspicions are right, that makes me 1/4 orc.